Given that $p$ is false and $q$ is false, let's evaluate the expression $p \land \neg q$.

Step 1: Identify the truth values

• $p = \text{false}$
• $q = \text{false}$

Step 2: Determine the truth value of $\neg q$

• $\neg q$ is the negation of $q$.
• Since $q = \text{false}$, $\neg q = \text{true}$.

Step 3: Evaluate $p \land \neg q$

• $p \land \neg q$ is the logical "and" of $p$ and $\neg q$.
• The "and" ($\land$) operation is true only if both operands are true.

In this case:

• $p = \text{false}$
• $\neg q = \text{true}$

Since one of the operands is false, $p \land \neg q$ is false.

Final Answer:

The truth value of $p \land \neg q$ is false.

Would you like more details or have any questions about this?

Here are some related questions to explore:

1. What is the truth table for the conjunction ($\land$) operation?
2. How does the truth value change if $p$ is true and $q$ is false?
3. What is the truth value of $\neg (p \land q)$ given $p = \text{false}$ and $q = \text{false}$?
4. How do logical operators like $\land$ and $\neg$ relate to circuits in computer science?
5. What happens if both $p$ and $q$ are true in the expression $p \land \neg q$?

Tip: When working with logical expressions, constructing a truth table can be a helpful way to visualize all possible outcomes.